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Minimum aberration and model robustness for two-level fractional factorial designs. (English) Zbl 0913.62072
Summary: The performance of minimum aberration two-level fractional factorial designs is studied under two criteria of model robustness. Simple sufficient conditions for a design to dominate another design with respect to each of these two criteria are derived. It is also shown that a minimum aberration design of resolution III or higher maximizes the number of two-factor interactions which are not aliases of main effects and, subject to that condition, minimizes the sum of squares of the sizes of alias sets of two-factor interactions.
This roughly says that minimum aberration designs tend to make the sizes of the alias sets very uniform. It follows that minimum aberration is a good surrogate for the two criteria of model robustness that are studied here. Examples are given to show that minimum aberration designs are indeed highly efficient.

MSC:
62K15 Factorial statistical designs
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